Methods and apparatuses for creating a statistical average model of an enamel-dentine junction

ABSTRACT

Disclosed is method and apparatus for creating a statistical average model of an enamel-dentine junction. The method includes steps of acquiring CT image data of a tooth; segmenting the CT image data to obtain a surface of an enamel-dentine junction; segmenting the obtained surface using a curvature-based clustering algorithm to remove a bottom of the enamel-dentine junction; spherical-parameterizing, by means of spherical harmonic analysis, the surface of the enamel-dentine junction after removal of the bottom; and aligning different samples of the tooth to obtain a statistical average model.

This application claims benefit of Serial No. 201310574340.0, filed 18Nov. 2013 in China and which application is incorporated herein byreference. A claim of priority is made to the above disclosedapplication.

TECHNICAL FIELD

The present disclosure relates to medical image processing, and moreparticularly, to methods and apparatuses for creating a statisticalaverage model of an enamel-dentine junction.

BACKGROUND

Aesthetic effects of natural tooth color and semi-transparent gradualchange are produced by superposing dental enamel and dentine with aninterface of enamel-dentine junction. To solve the problem that beautyand strength cannot be guaranteed at the same time for pure-zirconiaceramic crown of molar tooth, one effective approach is to develop atype of zirconia ceramic which has a gradient gradual change in opticalcolor and can be processed with Computer Aided Design (CAD)/ComputerAided Manufacturing (CAM), by simulating structure and opticalcharacteristics of the tooth. Basis for such structure simulation is tolearn a complete modality of the curved surface of the enamel-dentinejunction. In the research of the enamel-dentine junction modality,Document 1 (Anthony J. Olejniczak, Lawrence B, et al. Quantification ofdentine shape in anthropoid primates[J]. Ann Anat, 2004, 186: 479-485)and Document 2 (Smith T. M, Olejniczak A. J, Reid D. J, et al. Modernhuman molar enamel thickness and enamel-dentine junction shape[J].Archives of Oral Biology, 2006, 51: 974-995) study a modality of theenamel-dentine junction in some axial plane of the tooth, and theobtained enamel-dentine junction is a line other than a plane. Document3 (Rodrigo Borges Fonseca, Francisco Haiter-Neto, Alfredo J.Fernandes-Neto, et al. Radiodensity of enamel and dentin of human,bovine and swine teeth[J]. Archives of Oral Biology, 2004, 49:919-922)acquires a complete curved surface of the enamel-dentine junctionthrough Micro-CT (Computed Tomography). Document 4 (Robert S,Corruceini. The Dentinoenamel Junction in Primates[J]. InternationalJournal of Primatology, 1987, 8(2): 99-114), Document 5 (Bertram S,Kraus. Morphologic relationships between enamel and dentin surfaces oflower first molar teeth[J]. J. D. Res, 1952, 31(2):248-256) and Document6 (Panaghlotis Bazos, Pascal Magne. Bio-emulation: biomimeticallyemulating nature utilizing a histo-anatomic approach; structuralanalysis[J]. The European journal of esthetic dentistry, 2011, 6(1):8-19) acquire a complete curved surface of the enamel-dentine junctionusing a method of selectively removing enamel with aciddemineralization. The two methods using Micro-CT and aciddemineralization can be applied only on isolated teeth but not livenatural teeth, because ray dose in Micro-CT is large, and the aciddemineralization method is destructive. As a result, it is difficult tocollect a number of samples required to establish an enamel-dentinejunction database. Document 7 (Xiaojing Wang. Research on feasibility ofcreating 3D mortality of enamel-dentine junction surface with cone-beamCT[D]. Peking University Health Science Center, Beijing, 2012) canacquire the mortality of enamel-dentine junction surface without toothdamage by using cone-beam CT scanning in combination with imagesegmentation technology.

Document 8 (Kurbad A. Three-dimensionally layered ceramic blocks[J]. IntJ Comput Dent, 2010, 13(4): 351-65) attempts to build a 3D laminatedstructure resembling a natural dental crown in a full-ceramic block. Theceramic block is structured so that the inner ceramic part emulates theoptical characteristics of dentine, the outer ceramic part emulates theoptical characteristics of enamel, and an interface between the twoparts is cone-shaped. This can emulate, to some extent,semi-transparency and gradual change in color of natural crown, while itis inaccurate to assume the enamel-dentine junction as cone-shaped.

A statistical shape model is a model created from corresponding sets ofmark points in surfaces of anatomic structures of interest in a singleindividual at different moments or between different individuals at thesame moment. Creation of the statistical shape model is on the premiseof acquisition of corresponding mark point sets between anatomicstructures. Document 9 (Shen L, Makedon F S. Spherical mapping forprocessing of 3-D closed surfaces. Image and Vision Computing, 24(7):743-761, 2006) proposes a Spherical Harmonic Description (SPHARM) whichdetermines correspondence between structures through normalization ofparametric space. Statistical modeling and analysis with SPHARM requirethat input grids should be genus-zero surfaces, i.e., the module shouldhave a spherical topology. The enamel-dentine junction, however, is aninterface between two different mineralized tissues of epithelium andextracellular matrix, and has an unclosed surface in a shell shape.

SUMMARY

There is a need for methods of creating a statistical average modulethat is applicable to an unclosed surface.

According to an aspect of the disclosure, a method for creating astatistical average model of an enamel-dentine junction is provided,comprising steps of: acquiring CT image data of a tooth; segmenting theCT image data to obtain a surface of an enamel-dentine junction;segmenting the obtained surface using a curvature-based clusteringalgorithm to remove a bottom of the enamel-dentine junction;spherical-parameterizing, by means of spherical harmonic analysis, thesurface of the enamel-dentine junction after removal of the bottom; andaligning different samples of the tooth to obtain a statistical averagemodel.

In an embodiment, the CT image data are segmented using the Level Setalgorithm.

In another embodiment, the clustering algorithm comprises the K-Meansalgorithm.

In a further embodiment, the spherical-parameterization is performedusing an optimized Control of Area and Length Distortions algorithm.

In an embodiment, the area and length distortion control algorithm isoptimized by adding weights.

In an embodiment, the method further comprises: applying sphericalharmonics Fourier expansion on the parameterized surface after thespherical-parameterization.

In an embodiment, the alignment is performed in a spherical coordinatesystem.

In an embodiment, the alignment is performed by means of the SPHARMRegistration with Iterative Closest Point (SHREC) algorithm.

With the method for creating an average model of the present disclosure,it is possible to describe an object surface using spherical harmonicsfunction in an unclosed surface, and establish correspondence of markpoint sets between structures. Accordingly, in case of the cone-beam CTscanning samples of isolated teeth, a statistical average modeldescribing the mortality of enamel-dentine junction surface can becreated with any damage to the teeth.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects of the present disclosure will be apparentand illustrated with reference to embodiments in the following. Infigures:

FIG. 1 illustrates a flowchart of a method embodiment according to thedisclosure;

FIG. 2 illustrates a schematic diagram of a segmented surface ofenamel-dentine junction according to a method embodiment of thedisclosure;

FIG. 3 illustrates a schematic diagram of a surface of enamel-dentinejunction with a bottom being separated according to a method embodimentof the disclosure;

FIGS. 4A, 4B, 4C and 4D illustrate comparison between sphericalparameterization according to a method embodiment of the disclosure andspherical parameterization not according to the disclosure; and

FIG. 5 illustrates a schematic diagram of an average model acquiredaccording to a method embodiment of the disclosure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The particular embodiments of the disclosure are described below indetails. It shall be noted that the embodiments herein are used forillustration only, but not limiting the disclosure. In the descriptionbelow, a number of particular details are explained to provide a betterunderstanding to the disclosure. However, it is apparent to thoseskilled in the art the disclosure can be implemented without theseparticular details. In other examples, well-known circuits, materials ormethods are not described so as not to obscure the disclosure.

Throughout the specification, reference to “one embodiment,” “anembodiment,” “one example” or “an example” means that the specificfeatures, structures or properties described in conjunction with theembodiment or example are included in at least one embodiment of thepresent disclosure. Therefore, the phrases “in one embodiment,” “in anembodiment,” “in one example” or “in an example” occurred at variouspositions throughout the specification may not refer to one and the sameembodiment or example. Furthermore, specific features, structures orproperties may be combined into one or several embodiments or examplesin any appropriate ways. Moreover, it should be understood by thoseskilled in the art that figures here are for the purpose ofillustration, and not necessarily drawn to scale. It should beappreciated that “connecting” or “coupling” a component to anothercomponent may mean that the component is directly connected or coupledto the other component, or there may be a component intervening betweenthem. On the contrary, “directly connecting” or “directly coupling” acomponent to another component mans that there is no interveningcomponent. Like reference signs refer to similar elements throughout thefigures. The term “and/or” used herein means any and all combinations ofone or more listed items.

FIG. 1 illustrates a flowchart of a method embodiment according to thedisclosure.

After acquiring Computerized Tomography (CT) image data of a tooth, theCT image data are segmented at step S100 to remove enamel in the surfacelayer, and reconstruct a 3D mortality of the surface of anenamel-dentine junction. In an embodiment, the well-known Level Setalgorithm based on Sparse Field may be used for the segmentation.

During the segmentation of the CT image, interception of the dentinewith a cube in a region of interest will cause the enamel-dentinejunction surface, which should have been opened, to become closed.However, if the bottom is included in acquiring the statistical averagemodel of the enamel-dentine junction, accuracy for the modeling will beconsiderably reduced. In the embodiment of the present disclosure, it isrequired to segment out the bottom and any possible pulp cavity, andthus reduce influence of the bottom and pulp cavity during the creationof statistical average model.

After reconstructing the 3D mortality of the enamel-dentine junctionsurface, the bottom is separated from the enamel-dentine junction usinga curvature-based clustering algorithm at step S200.

In an embodiment of the present disclosure, a triangular grid model isused to emulate the enamel-dentine junction surface. The triangular gridmodel M may be represented by a pair of linear sets:M=(V,F)

V={ν_(i):l≤i≤n_(V)} denotes a set of vertices, and n_(V) is the numberof vertices. F={f_(k):l≤k≤n_(F)} denotes a set of triangular patches,and is the number of triangular patches.

In order to implement the curvature-based clustering algorithm, it isnecessary to compute normal vectors at the vertices of the triangulargrid model, and compute curvatures at the vertices of the triangulargrid model based on these normal vectors.

The normal vectors at the vertices may be computed as follows.

Assuming that a vertex of the triangular grid model is denoted as ν_(i),and a set of vertices except the vertex ν_(i) is denoted as V^(i). Avertex ν_(j) is a neighbor point of ν_(i) if ν_(j)ϵV^(i). The number ofvertices in V^(i) is denoted as |V^(i)|. A set of triangular patchesincluding ν_(i) is denoted as F^(i). f_(k) is associated with ν_(i) ifthe triangular patch f_(k)ϵF^(i). The number of triangular patches inF^(i) is denoted as |F^(i)|.

To reflect influence of the shape of the triangular patch on the normalvector at the vertex, the normal vector N_(ν) _(i) at the vertex ν_(i)is computed with Equation (1):

$\begin{matrix}{N_{v_{i}} = \frac{\sum\limits_{f_{k} \in F^{i}}\;{\gamma_{k}A_{k}N_{f_{k}}}}{{{\sum\limits_{f_{k} \in F^{i}}\;{\gamma_{k}A_{k}N_{f_{k}}}}}}} & (1)\end{matrix}$

γ_(k) is an interior angle of f_(k) at the vertex ν_(i), Ak is an areaof the triangular patch f_(k), and N_(f) _(k) is the normal vector ofthe triangular patch f_(k) and is determined with Equation (2):

$\begin{matrix}{N_{f_{k}} = {\frac{e_{i,{j + 1}} \times e_{ij}}{{{e_{i,{j + 1}} \times e_{ij}}}} = \frac{\left( {v_{i} - v_{j + 1}} \right) \times \left( {v_{i} - v_{j}} \right)}{{{\left( {v_{i} - v_{j + 1}} \right) \times \left( {v_{i} - v_{j}} \right)}}}}} & (2)\end{matrix}$

e_(i,j+1) denotes a edge vector pointing from the vertex ν_(j+1) to thevertex ν_(i).

After computation of the normal vector at the vertex, the curvature atthe vertex of the triangular grid is computed as follows.

A tangent plane at a vertex is first computed, and then vertices in theneighborhood of the vertex are projected onto the tangent plane. Thenormal vector N_(ν) _(i) at the vertex ν_(i) is, and a plane having thenormal vector N_(ν) _(i) and passing the vertex ν_(i) is the tangentplane, denoted as

N_(ν) _(i)

^(⊥), at the vertex ν_(i). A vertex ν_(j) in the neighborhood of thevertex ν_(i) is projected onto the tangent plane as ν_(j) ^(⊥).

A unit tangent vector T_(ij) of the vertex ν_(i) in the tangent plane

N_(ν) _(i)

^(⊥) along a direction of ν_(i)ν_(j) ^(⊥) is:

$\begin{matrix}{T_{ij} = \frac{{\left\langle {N_{v_{i}},{v_{j} - v_{i}}} \right\rangle N_{vi}} - \left( {v_{j} - v_{i}} \right)}{{{{\left\langle {N_{v_{i}},{v_{j} - v_{i}}} \right\rangle N_{vi}} - \left( {v_{j} - v_{i}} \right)}}}} & (3)\end{matrix}$

< > denotes a dot product of two vectors.

A symmetric matrix M_(ν) _(i) is computed with the unit tangent vector:

$\begin{matrix}{M_{v_{i}} = {{\sum\limits_{v_{j} \in V^{i}}\;{w_{ij}k_{ij}{T_{ij}\left( T_{ij} \right)}^{T}}} = \begin{bmatrix}m_{v_{i}}^{11} & m_{v_{i}}^{12} & m_{v_{i}}^{13} \\m_{v_{i}}^{21} & m_{v_{i}}^{22} & m_{v_{i}}^{23} \\m_{v_{i}}^{31} & m_{v_{i}}^{32} & m_{v_{i}}^{33}\end{bmatrix}}} & (4)\end{matrix}$

$w_{ij} = \frac{A_{f_{k}}}{\sum\limits_{f_{k} \in F^{i}}A_{f_{k}}}$is a weight, T_(ij) is the unit tangent vector at the vertex ν_(i), and

$k_{ij} = \frac{2\left\langle {N_{v_{i}},{v_{j} - v_{i}}} \right\rangle}{{{{v_{j} - v_{i}}}}^{2}}$is a curvature at the vertex ν_(i) along a direction of T_(ij).

The symmetric matrix M_(ν) _(i) has two eigenvalues m_(ν) _(i) ¹¹ andm_(ν) _(i) ²². Document 10 (G. Taubin. Estimating the tensor ofcurvature of a surface from a polyhedral approximation[A]. In: WELGrimson ed. Proceedings of the Fifth International Conference onComputer Version[C], Los Alamitos: IEEE Computer Society Press, 1995:902-907) describes equations for solving the principal curvatures at thevertex ν_(i) based on the two eigenvalues:k _(ν) _(i) ¹=3m _(ν) _(i) ¹¹+8m _(ν) _(i) ²²k _(ν) _(i) ²=3m _(ν) _(i) ²²+8m _(ν) _(i) ¹¹  (5)

As such, the principal curvature values k₁, k₂ and correspondingcurvature directions d₁, d₂ can be obtained for each vertex of thetriangular grid.

Following the obtaining of the curvatures for vertices, the vertices maybe clustered based on the curvatures. In an embodiment of the presentdisclosure, the K-Means algorithm may be used to cluster the vertices ofthe triangular grid by distance based on the principal curvature values(i.e., Euclidean distance in curvature space). Two objects are firstselected at random as centers for clustering, as initial clusters. Then,the data set composed of the principal curvature vector (k₁, k₂) isclustered in each iteration. Particularly, for each object remaining inthe data set, the object is reassigned to a closest cluster according toa distance between the object to each of the cluster centers. Havingprocessing all data objects, one iteration is completed, and new clustercenters are obtained. Each of the vertices in the triangular grid willbe classified into cluster at the end of the algorithm. The bottom canbe separated from the enamel-dentine junction surface with thecurvature-based clustering algorithm. FIG. 3 shows a schematic diagramof separating the bottom from the enamel-dentine junction surface withthe clustering algorithm. In FIG. 3, the darkest part represents theseparated bottom which is composed of a triangular grid.

After removal of the bottom, spherical-parameterization, by means ofspherical harmonic analysis, is applied to the surface of theenamel-dentine junction without the bottom at step S300.

In the process, spherical-parameterization of the patch model is firstperformed with an optimized Control of Area and Length Distortions(CALD) algorithm. Document 9 (Shen L, Makedon F S. Spherical mapping forprocessing of 3-D closed surfaces. Image and Vision Computing, 24(7):743-761, 2006) describes the CALD algorithm, which is optimized in themethod of the present disclosure.

For the model of the entire triangular grid, the cost C_(a)(M,Ψ) of areadistortion in the parameterization is:

$\begin{matrix}{{C_{a}\left( {M,\Psi} \right)} = \frac{\sum\limits_{t_{i} \in M}\;\left\lbrack {{\max\left( {\frac{A\left( {\Psi\left( t_{i} \right)} \right)}{A\left( t_{i} \right)},\frac{A\left( t_{i} \right)}{A\left( {\Psi\left( t_{i} \right)} \right)}} \right)} \times {A\left( {\Psi\left( t_{i} \right)} \right)} \times {ɛ\left( t_{i} \right)}} \right\rbrack}{A\left( {\Psi(M)} \right)}} & (6)\end{matrix}$

M={t_(i)} represents a set of triangles in the original model in theCartesian coordinate system. Ψ is a reversible map for mapping thetriangles M into a grid in the parametric space, i.e., Ψ(M)={Ψ(t_(i))}.A(⋅) represents the area of the triangle or the grid in the parametricspace.

Here, ε(t_(i)) represents a weight and defined with Equation (7):

$\begin{matrix}{{ɛ\left( t_{i} \right)} = \left\{ \begin{matrix}w & {t_{i} \in B} \\1.0 & {t_{i} \in T}\end{matrix} \right.} & (7)\end{matrix}$

B is a set of triangles at the bottom, and T=M−B is a set of trianglesin the original model except the bottom.

Influence of the bottom area in the parameterization process is reducedby adding the weight ε(t_(i)). FIGS. 4A and 4B show results of thespherical parameterization without addition of the weight, and FIGS. 4Cand 4D show results of the spherical parameterization with addition ofthe weight. As can be seen from FIGS. 4A, 4B, 4C and 4D, for the regionother than the bottom, the spherical mapping can map the grid oftriangles onto a unit sphere in a continuous and uniform manner. For thebottom region, there will be more area distortion in mapping in order tominimize area distortion in the mapping of the non-bottom region.

After the spherical parameterization, a spherical harmonics Fourierexpansion is applied to the result of the parameterization to obtain aspherical harmonics function expansion form. The spherical harmonicsfunction Y_(l) ^(m)(θ,ϕ)(−l≤m≤l) is a set of functions which are definedin the spherical coordinate system and constitute a set of normalizedorthogonal bases on a sphere. The spherical harmonics descriptor isparameterized so that any single-connected curved topology structure isequivalent to a sphere. A point ν(θ, ϕ) on the sphere may be representedby a linear combination of the spherical harmonics functions:

$\begin{matrix}{{v\left( {\theta,\phi} \right)} = {\sum\limits_{l = 0}^{\infty}\;{\sum\limits_{m = {- l}}^{l}\;{c_{l}^{m}{Y_{l}^{m}\left( {\theta,\phi} \right)}}}}} & (8)\end{matrix}$

c_(l) ^(m)=(c_(xl) ^(m),c_(yl) ^(m),c_(zl) ^(m))^(T) may be calculatedby the least-square estimation. c_(l) ^({circumflex over (m)}) is anestimate of the original coefficient c_(l) ^(m). The original functionmay be restored as follows:

$\begin{matrix}{{\hat{v}\left( {\theta,\phi} \right)} = {{\sum\limits_{l = 0}^{L_{{ma}\; x}}{\sum\limits_{m = {- l}}^{l}{\hat{c_{l}^{m}}{Y_{l}^{m}\left( {\theta,\phi} \right)}}}} \approx {v\left( {\theta,\phi} \right)}}} & \;\end{matrix}$

L_(max) is the maximal degree of freedom specified by a user. The largerL_(max) is, the more accurate the restored {circumflex over (ν)}(θ,ϕ)is.

The parameterization of the model is achieved after spherical harmonicsrestoration is performed for the vertices of the triangular grid.

Finally at step S400, different samples of the same individual tooth arealigned to acquire a statistical average model for the tooth. FIG. 5shows the statistical average model of the enamel-dentine junction of apremolar tooth.

In an embodiment of the present disclosure, alignment between the samplemodel space and the parametric space is performed with the SHREC (SPHARMRegistration with Iterative Closest Point) algorithm known from Document11 (Shen, L., Huang, H., Makdeon, F., Saykin, A. J.: Efficientregistration of 3D spharm surface. In: 4th Canadian Conf. on Computer &Robot Vision. (2007) 81-88), and thus correspondence between differentsample models may be established. In an example, 45 isolated-toothsamples may be collected to create the statistical average model of theenamel-dentine junction of the first premolar tooth. Use of the SHRECalgorithm allows automatic positioning of corresponding mark point setsfor the same structure between different individuals.

With the method of the present disclosure, it is possible to create astatistical average model for an unclosed surface. Further, the methodcan obtain a 3D statistical average model from cone-beam CT image of anyother object.

The method of the present disclosure may be implemented in computersoftware, computer hardware or combination thereof.

The foregoing detailed description has set forth various embodiments ofmethod and apparatus for creating a statistical average model of anenamel-dentine junction by use of block diagrams, flowcharts, and/orexamples. Insofar as such block diagrams, flowcharts, and/or examplescontain one or more functions and/or operations, it will be understoodby those skilled in the art that each function and/or operation withinsuch examples may be implemented, individually and/or collectively, by awide range of hardware, software, firmware, or virtually any combinationthereof. In one embodiment, several portions of the subject matterdescribed herein may be implemented via Application Specific IntegratedCircuits (ASICs), Field Programmable Gate Arrays (FPGAs), digital signalprocessors (DSPs), or other integrated formats. However, those skilledin the art will recognize that some aspects of the embodiments disclosedherein, in whole or in part, may be equivalently implemented inintegrated circuits, as one or more computer programs running on one ormore computers (e.g., as one or more programs running on one or morecomputer systems), as one or more programs running on one or moreprocessors (e.g., as one or more programs running on one or moremicroprocessors), as firmware, or as virtually any combination thereof,and that designing the circuitry and/or writing the code for thesoftware and or firmware would be well within the skill of those skilledin the art in light of this disclosure. In addition, those skilled inthe art will appreciate that the mechanisms of the subject matterdescribed herein are capable of being distributed as a program productin a variety of forms, and that an illustrative embodiment of thesubject matter described herein applies regardless of the particulartype of signal bearing medium used to actually carry out thedistribution. Examples of a signal bearing medium include, but are notlimited to, the following: a recordable type medium such as a floppydisk, a hard disk drive, a Compact Disc (CD), a Digital Versatile Disk(DVD), a digital tape, a computer memory, etc.; and a transmission typemedium such as a digital and/or an analog communication medium (e.g., afiber optic cable, a waveguide, a wired communications link, a wirelesscommunication link, etc.).

While the present disclosure has been described with reference toseveral typical embodiments, it is apparent to those skilled in the artthat the terms are used for illustration and explanation purpose and notfor limitation. The present disclosure may be practiced in various formswithout departing from the esprit or essence of the disclosure. Itshould be understood that the embodiments are not limited to any of theforegoing details, and shall be interpreted broadly within the espritand scope as defined by the following claims. Therefore, Modificationsand alternatives falling within the scope of the claims and equivalentsthereof are to be encompassed by the scope of the present disclosurewhich is defined by the claims as attached.

What is claimed is:
 1. A method of processing image data of a tooth forproducing a physical tooth model that simulates structural and opticalcharacteristics of the tooth, the method comprising: acquiring, by aComputerized Tomography (CT) machine, CT image data of a tooth;segmenting, by a computer, the CT image data to obtain a surface of anenamel-dentine junction of the tooth; segmenting, by the computer, theobtained surface using a curvature-based clustering algorithm to removea bottom of the enamel-dentine junction, wherein a triangular grid modelis used to emulate the enamel-dentine junction, and wherein saidcurvature-based clustering algorithm comprises computing normal vectorsat the vertices of the triangular grid model and computing curvatures atthe vertices of the triangular grid model based on these normal vectors;spherical-parameterizing, by the computer and by means of sphericalharmonic analysis, the surface of the enamel-dentine junction afterremoval of the bottom; and aligning, by the computer, different samplesof the tooth to create a statistical average model of the enamel-dentinejunction; wherein the statistical average model of the enamel-dentinejunction is used to produce the physical tooth model of the tooth, sothat the tooth model simulates structural and optical characteristics ofthe tooth.
 2. The method according to claim 1, wherein the CT image dataare segmented using the Level Set algorithm.
 3. The method according toclaim 2, wherein the clustering algorithm comprises the K-Meansalgorithm.
 4. The method according to claim 3, wherein thespherical-parameterization is performed using an optimized Control ofArea and Length Distortions algorithm.
 5. The method according to claim4, wherein the Control of Area and Length Distortions algorithm isoptimized by adding weights.
 6. The method according to claim 1, furthercomprising: applying spherical harmonics Fourier expansion on theparameterized surface after the spherical-parameterization.
 7. Themethod according to claim 6, wherein the alignment is performed in aspherical coordinate system.
 8. The method according to claim 1, whereinthe alignment is performed by means of the SPHARM Registration withIterative Closest Point (SHREC) algorithm.
 9. An apparatus forprocessing image data of a tooth for producing a physical tooth modelthat simulates structural and optical characteristics of the tooth, theapparatus comprising: a Computerized Tomography (CT) machine configuredto acquire CT image data of a tooth; a computer configured to create astatistical average model of an enamel-dentine junction of the tooth bysegmenting the CT image data to obtain a surface of the enamel-dentinejunction; segmenting the obtained surface using a curvature-basedclustering algorithm to remove a bottom of the enamel-dentine junction,wherein a triangular grid model is used to emulate the enamel-dentinejunction, and wherein said curvature-based clustering algorithmcomprises computing normal vectors at the vertices of the triangulargrid model and computing curvatures at the vertices of the triangulargrid model based on these normal vectors; spherical-parameterizing, bymeans of spherical harmonic analysis, the surface of the enamel-dentinejunction after removal of the bottom; and aligning different samples ofthe tooth to obtain the statistical average model; wherein thestatistical average model of the enamel-dentine junction is used toproduce the physical tooth model of the tooth, so that the tooth modelsimulates structural and optical characteristics of the tooth based.